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Gödel's theorem --- Mathematical recreations

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Gödel's theorem --- Gödel, Théorème de

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Mathematicians from Leibniz to Hilbert have sought to mechanise the verification of mathematical proofs. Developments arising out of Gödel's proof of his incompleteness theorem showed that no computer program could automatically prove true all the theorems of mathematics. In practice, however, there are a number of sophisticated automated reasoning programs that are quite effective at checking mathematical proofs. Now in paperback, this book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including Gödel's incompleteness theorem and the Church-Rosser theorem. The computer verification using the Boyer-Moore theorem prover yields precise and rigorous proofs of these difficult theorems. It also demonstrates the range and power of automated proof checking technology. The mechanisation of metamathematics itself has important implications for automated reasoning since metatheorems can be applied by labour-saving devices to simplify proof construction. The book should be accessible to scientists and philosophers with some knowledge of logic and computing.

Gödel's theorem --- Automatic theorem proving. --- Data processing.

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"The first major biography of the logician and mathematician whose incompleteness theorems helped launch a modern scientific revolution. Nearly a hundred years after its publication, Kurt Gödel's famous proof that every mathematical system must contain propositions that are true-yet never provable-continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life. An intimate portrait of the scientific and intellectual circles in prewar Vienna and a vivid re-creation of the early days of Princeton's Institute for Advanced Study, Journey to the Edge of Reason is the first biography to fully draw upon Gödel's voluminous letters and writings-including a never-before-transcribed shorthand diary of his most intimate thoughts-to explore his profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It illuminates the mind-bending implications of Gödel's revolutionary ideas for philosophy, mathematics, artificial intelligence, and man's place in the cosmos."

Logicians --- Mathematician --- Gödel's theorem --- Mathematics --- Logic, Symbolic and mathematical --- Gödel, Kurt

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Gödel's theorem --- Logic, Symbolic and mathematical --- Gödel, Théorème de --- Logique symbolique et mathématique